Equivalently, a perfect number is a number that is half the sum of all of its positive divisors (including itself) i.e. σ1(n) = 2n. So one can easily define an algorithm to check for perfect numbers :

May 3, 2023 · In this other question, somebody mentions that in a letter to Mersenne dated November 15, 1638, Descartes showed that D =32 ⋅72 ⋅112 ⋅132 ⋅ 22021 = 198585576189 D = 3 2 7 2 11 2 13 …

I came up with these: Applications of Mersenne numbers: signed/unsigned integers, towers of Hanoi Applications of Fermat numbers: relation to constructible polygons But for perfect numbers the best I …

4 Question: Show that all even perfect numbers end in 6 or 8. This is what I have. All even perfect numbers are of the form n =2p−1(2p − 1) n = 2 p 1 (2 p 1) where p p is prime and so is (2p − 1) (2 p 1).

A well known theorem by Euler states that every even perfect number is of the form $2^ {p-1} (2^p-1)$ where $2^p-1$ is prime (this is what is called a Mersenne prime).

Dec 5, 2019 · There has been a lot of work done on this topic, enough so it is hard to summarize in a forum like this. If you search for odd perfect number you will find a lot of information. Some of it is …

@user129901 A proof of Euler's result that all even perfect numbers are in fact of the form (the form that Euclid knew), can be found online several places, for example A proof that all even perfect numbers …

Oct 16, 2018 · A perfect number is a number than can be expressed as a sum of its factors. For example, 28 = 1 + 2 + 4 + 7 + 14 Why is this property important? What is so perfect about perfect …

The question Are there infinitely many perfect numbers? is a classic old unsolved problem. However, we keep finding perfect numbers (via Mersenne primes) and produce a lot of knowledge on perfect n...

Nov 22, 2024 · The only prime divisors of an (even) perfect number are $2$ and the Mersenne prime associated with the perfect number. What are you asking?